Generation of phase shift maps for subsurface inclusions in a nanocomposite to train machine learning models in atomic force microscopy

Abstract

Quality control of nanofiller distribution (carbon nanotubes, carbon black) is crucial for the properties of polymer nanocomposites. The existing methods of atomic force microscopy (AFM) allow for indirect assessment of the distribution via two-dimensional phase contrast maps, whereas more accurate three-dimensional techniques require either lengthy experiments or resource-intensive finite element (FE) modeling, which limits their practical application. This paper presents an approach to creating a synthetic dataset that will eventually allow the use of machine learning methods for accelerating the reconstruction of filler distribution patterns based on AFM phase-contrast data. The generation of a synthetic database for training the neural network is accomplished in the MATLAB environment and involves the variation of key parameters: particle geometry and depth, probe shape, and elastic and surface-energy properties of the materials. Data acquisition requires calculating the relationship between the particle depth and the phase shift determined by the tapping-mode AFM technique. The generated dataset reveals a direct correlation between the surface phase portraits (the standard tapping-mode AFM output signal) and the three-dimensional distribution of inclusions in the subsurface layer. The study demonstrates the influence of geometric parameters (particle radius, depth, probe radius) on the quality and appearance of theoretical dissipation maps. It has been found that there is a nonlinear relationship between the depth of the filler particles and the dissipative losses causing a phase shift, which makes it possible to eliminate the ambiguities during the reconstruction of the structure. The obtained results open possibilities for rapid quantitative analysis of nanocomposites and, in the longer term, for consideration of more complex filler morphologies (agglomerates, chain-like structures).